We presented a distributional Motohashi's formula at this number theory seminar 3 years ago. We will briefly present a refined/published version of this formula. Based on this version, applications to the uniform Weyl-type subconvex bounds for some $PGL(2)$ $L$-functions, as well as the limitation of the method, will be discussed. These results are joint works with Balkanova--Frolenkov and Ping Xi, respectively. If time permits, we will present a further application to the partition function, joint work with Nicholas Andersen.